The Ladder Construction of Prüfer Modules

let be a ring (associative, with 1). a non-zero module is said to be a prüfer module provided there exists a surjective, locally nilpotent endomorphism with kernel of finite length. the aim of this note is to construct prüfer modules starting from a pair of module homomorphisms , where is injective and its cokernel is of finite length. for the ring of integers, one can construct in this way the ordinary prüfer groups considered in abelian group theory. our interest lies in the case that is an artin algebra.